Infrared detection and imaging systems detect the amount of radiation generated by a target. Any target having a temperature greater than 0.degree. K can emit radiation in the form of infrared signals. Accordingly, the infrared detection and imaging systems generate an image of temperatures of the target or a "thermal image" of the target. Infrared detection and imaging systems often employ focal plane arrays or "FPAs" to generate these "thermal images". For example, these infrared detection and imaging systems are widely used in the military for target detection and tracking. The FPA includes a plurality of detectors arranged in rows and columns. Each detector detects infrared signals and converts the infrared signal into a corresponding electrical signal. A detector's responsibility is defined as the relationship between the received infrared signal level and the corresponding electrical signal generated by the detector.
The responsibility of each detector in a FPA is dependent on the process employed to make that detector and also on the bias provided to the detector. Accordingly, across the FPA, differences in the process and bias cause the responsibility of the detectors to vary. This variation of the responsibility of the detectors causes errors, such as fixed pattern noise in the infrared detection and imaging system. Fixed pattern noise is undesirable in imaging systems because the fixed pattern noise causes the degradation of temperature resolution of the imaging systems (i.e., increases the minimum resolvable temperature difference (MRTD) of the imaging systems).
Moreover, the variation of the responsibility of the detectors degrades the temperature resolution of the system resulting in loss of detail, contrast, and quality in the thermal image. Accordingly, the electrical signal generated by the FPA must first be corrected by software or hardware to account for the non-uniformity of process and bias across the FPA.
A first known approach to non-uniformity correction employs a two-point or multi-point linear correction method. One advantage of this approach is that only two correction parameters need to be stored for each detector thereby simplifying the implementation of this approach. This approach provides good results if the response of the detectors varies in a linear fashion with respect to the target temperature (i.e., if the graph of the target temperature versus electrical signal generated by the detector is linear). Unfortunately, the response of the detectors often varies in a non-linear fashion with respect to target temperature. For detectors with a non-linear response, this first approach provides poor results with relatively large error, which may be unacceptable. For more information about this first approach, please see Y. Gao, M. Wu, Q. Shou, Chinese Journal of Infrared and Millimeter Wave 12, 169 (1993).
A second known approach to non-uniformity correction employs a piece-wise linear correction method. The piece-wise linear correction method first divides the responsibility curve (i.e., temperature vs. electrical signal graph) into one or more intervals. Each interval is then approximated by a line. Unfortunately, the piece-wise linear correction method has two disadvantages. First, there are many more correction parameters that need to be stored as compared to the first method. For example, if the number of intervals is n, then for each detector, 2n number of parameters need to be stored. Second, the temperature interval to which the response signal of the detector belongs needs to be decided so that the right correction parameters can be selected.
A third known approach, also known as Schulz's approach, to non-uniformity correction employs a polynomial fitting method. This method is suited for FPA detectors having non-linear photo-response characteristics. The basic principle of Schulz's approach is to fit .DELTA.Y.sub.j (i.e., the difference between a detected signal of each detector and a mean response signal &lt;Y&gt; of all N detectors to a same target) by an n-th order polynomial of &lt;Y&gt;.
Schulz's primary expression is as follows: ##EQU1##
where (j=1, 2, . . . N).
The fitting coefficients a.sub.ij can be obtained from measured data of the detectors at several points in a range of target temperatures. We can solve the above expression for &lt;Y&gt; and get EQU &lt;Y&gt;.apprxeq.F.sub.j (Y.sub.j), where (j=1, 2, . . . N).
Since the value of Y.sub.j after correction should be &lt;Y&gt;, the correction expression of Y.sub.j is EQU Y.sub.j.sup.c =F.sub.j (Y.sub.j), where (j=1, 2, . . . N).
For a correction order of n=0, the correction expression is as follows: EQU Y.sub.j.sup.c =Y.sub.j -a.sub.0j, where (j=1, 2, . . . N).
For a correction order of n=1, the correction expression is as follows: ##EQU2##
where (j=1, 2, . . . N.
For a correction order of n=2, the correction expression is as follows: ##EQU3##
where (j=1, 2, . . . N). For more information about this third approach, please see M. Schulz and L. Caldwell, Infrared Physics & Technology 36, 763 (1995).
This third method overcomes the disadvantages of the piece-wise linear approach. However, this third method has the following disadvantages: (1) it requires division and root extraction operations, such as square root operations; (2) it generates non-analytic correction expressions when the correction order (n) is greater than or equal to three; (3) it involves having to select correct roots from multiple roots expressions when the correction order (n) is greater than one; and (4) the correction expression, even for n=2, is complex to implement. These complexities are further compounded when the correction order is increased above two.
Based on the foregoing, there remains a need for an improved method and apparatus for correction of non-uniformity in focal plane arrays that overcomes the disadvantages discussed previously.